As someone who is working with the winter theme for several years now, I feel partially obligated to chime in.
Really, really cold weather is a complex stuff. It introduces several complications to things that otherwise would be really straigthforward. I could talk about several diferent factors that one should take into account while creating something like this, but for now I will focus on your energy issue, to keep the scope to the question.
Why do we need power?
Power, be it in the form of heat from a fire or generated by some electric means, is crucial to any kind of more civilized human population. You use it to warm up your kids when it's cold, to work metal, to prepare food, to light up your village when it's dark. We need power to run our machines, to power our vehicles. You need some form of energy to do almost anything more complex on a human settlement, and from where that power comes from really makes a difference.
Conversion = Loss
Anything you do with your avaliable power source will reduce the avaliable amount of power, be it converting it from one form to another, transfering it or just storing it. Even the most advanced batteries we have today can't really store energy forever, losing it slowly over time.
While the sun generates a ton of power [citation needed], you can't exactly tap on it without some big losses.
Let's take this site into account, and do some quick math.
According to this site, the global formula to estimate the electricity generated in output of a photovoltaic system is something like this:
E = A * r * H * PR
Where:
E = Energy (kWh)
A = Total solar panel Area (m²)
r = solar panel yield (%)
H = Annual average solar radiation on tilted panels (shadings not included)
PR = Performance ratio, coefficient for losses (range between 0.5 and 0.9, default value = 0.75)
So, let's start.
Lets suppose that, somehow, your airship have $9000$ square feet $(30ft\times 300ft)$ of usable solar-colecting area. That's a really big airship, according your parameters. That gives us around $850m^2. $
My source says that Norway receives around $200\text{kWh}$ per square meter... per year. So, let's do a really crude math and split that evenly year-around:
- $200 / 365$ $\approx = 0.55\text{kWh}/m^2$ per day of solar exposure, assuming $100\%$ efficiency.
Most commom modern solar panels of the have something around $15\%$ of efficiency collecting solar power, using advanced manufactoring processes.
That means that a $1m^2$ worth of modern solar panels on a norway-like have a daily output of:
- $0.55 \times 0.15 = 0.0825$ $\text{kWh}$ per square meter per day.
Performance Ratio takes into account disturbances to the solar panels, like dust, snow, a few clouds, power losses generated by the internal structure of the solar panels, and things like that. The default value for modern solar powers is $0.75$. So, taking that into account:
- $0.0825 \times 0.75 \approx= 0.062 \text{kWh}$ per square meter per day. That's around 62 Wh per day per $m^2$.
You could use a light bulb for something like an hour!
So, let's equip our airship with a ton of solar panels.
$0.062kWh/m^2 \times 850 m^2 = 52.7 \text{kWh}$ worth of power on a daily basis.
If you devise a super efficient electric heater that uses 1kWh per family (normal heaters use around 1.5kWh to heat a single room) , and keep it on for a full day, one of such ships can only suply the heat demands of two houses.
You would need several airships to power all the houses on your village confortably. Each 850m² airship could power:
- The daily heating needs for 2 houses, or
- 36 modern 60w Ligth Bulbs for a day, or
- 42 10-minutes baths using a 7500w shower, or
- Cook food per 30 minutes 20 times a day using an electric oven.
Most people around the world that really needs heat use some type of oil for heating and coal or gas for cooking. Electric power, while convenient, can become expensive really quick if you don't keep an eye on your usage. I think that, if you want those things to fly around AND power your houses, each family would need at least one 850m² airship.
Also, your airships would be really heavy. Since you don't have wood, you would need some type of ligth material to build then, and a huge amount of power to make them take off. Unless you use some kind of heated gas, like helium, to make them "ligther than air", they can't really fly solar-powered. And, if they do have some gas to make them lighter, they would be really, really propense to accidents, and you can't repair them anymore since you don't have the resources to build them!
I would like to contribute a bit more to your scenario with some extra considerations:
The Major issues:
- So far north, during an Ice Age, you have an ice sheet. Plant's can't grow on ice sheets, since the soil is far away from the surface.
- Your people don't have wood. You can't grow trees on an ice sheet!
- Your people don't have paper. Since you don't have trees, unless they write directly in leather or stone, they don't really have anything to write on.
- You don't have rubber or easy access to any insulating material, so... that would be a huge problem.
- All of your homes would be glacialy cold. Again, since you don't have wood, you would need to build houses out of stone. I don't have any idea about how they would build such houses.
- Your people can't really mine for any type of mineral. You can't work almost any metal with such tech without fossil fuels or some other type of non-electric power. Since you can't work metal, you can't create the tools needed for true mining.
- Even if at somepoint your people had something avaliable to create tools, tools need constant replacement. They break, become dull, rust, etc. Bone tools only take you so far, you need true metal tools for complex works.
- You don't have any type of cloth avaliable, only leather. Even if you had sheeps, you won't be able to shear them (missing tools) or weave the wool (can't build the machinery to weave it).
- You don't have inks. Since you can't mine and can't really travel, unless you have a ton of exotic, colorful herbs that grow on the extreme cold, your people can't relly color stuff.
- Food is an issue. You basically only have meat for food, and you can't hunt. Your people can't use guns, since they lack the minerals to create them, and they can't use bows, since you don't have wood or other suitable material. You can't use spears, to - no wood! Caribou are really fast animals, and even a baby-caribou can run extremelly fast. Unless your people hunt using stone knives and ambush tatics, your people have some problems. Actually, I don't even know what your caribou would eat, since you can't have any type of plant matter on the surface of an ice sheet.
- You don't have glass. Even if you indeed have sand, you can't create a furnace to melt the sand to create glass. That means, among other things, that you also don't have any kind of lightbulb around anymore.
- It is not possible to have a SolarImpulse-class engine with your avaliable tech. To manufature such engine, you need all the tech around it - which includes high precision, automated manufactoring and advanced eletronics.
My suggestion to you is, if you really want to focus on airship travel, to create a canyon-based world. That way you can use all the normal stuff - trees, fossil fuels, etc, while still barring overland and aquatic transport. People would live on the top of extremely high and extremly steep canions (something like this, just way higher), so they really would need airships to move around if the canions are complex enough. Also, if you create them high enough, they could be way above the clouds, so you can't really see what's down there.
Just my 2¢!